# PRIM-cipal components analysis

arXiv: https://arxiv.org/abs/2604.15538 · HTML: https://mlsanity.com/paper/2604.15538/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 27 references that are in the map.
- First posted on arXiv 16 Apr 2026.

## Builds on (most cited first, 8 of 8)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [The Futility of Bias-Free Learning and Search](https://mlsanity.com/paper/1907.06010/) (2019)
- [Modal Principal Component Analysis](https://mlsanity.com/paper/2008.03400/) (2020)
- [Mode hunting through active information](https://mlsanity.com/paper/2011.05794/) (2020)
- [Is it possible to know cosmological fine-tuning?](https://mlsanity.com/paper/2401.04190/) (2024)
- [Unsupervised Bump Hunting Using Principal Components](https://mlsanity.com/paper/1409.8630/) (2014)
- [Statistical learning does not always entail knowledge](https://mlsanity.com/paper/2501.01963/) (2024)
- [Conserved active information](https://mlsanity.com/paper/2512.21834/) (2025)

## Abstract (arXiv)

Supervised No Free Lunch Theorems (NFLTs) are well studied, yet unsupervised NFLTs remain underexplored. For elliptical distributions, we prove that there exist two equally optimal, scientifically meaningful bump-hunting strategies that are exact opposites, with no universal winner. Specifically, peeling k orthogonal dimensions from ℝd (d ≥ k), retaining an inter-quantile region of probability 1-α per peeled dimension, maximizes total variance and Frobenius norm when the k smallest principal components (called pettiest components) are selected, and minimizes them when the selected dimensions are the k leading principal components. These optima inspire PRIM-based bump-hunting algorithms either by minimizing variance or by minimizing volume, thereby motivating an NFLT. We test our results on the Fashion-MNIST database, showing that peeling the largest principal components captures multiplicity, while peeling the smallest principal components isolates popular styles.